Hey Kutten, there are three ways that a dealership makes money on a car deal. They can make money on the car they're selling, they can make money on the car that is traded in, and they can make money on financing and insurance products that the customer buys. I'm not sure about the laws of TX, but it sounds like the car deal wasn't consumated yet. If the deal hasn't been consumated they can usually back out of the deal, just like you can usually back out of it. Mostly, to consumate a deal, there has to be a sale, financing of the car, and the customer has to take delivery i.e. drive it off the lot. They probably sold the Civic a lot cheaper than they wanted to, but knew they would make the money back by the higher APR. When you came back with your own financing, they weren't goin to make any money, so they decided to back out.
I'm not a lawyer, nor am I trained in F&I. Anyone else that wants to jump in, go right ahead :D
Hope this helps